Re: [EM] Recursive Elimination Supervisor
Tony, I am a little worried that this simplification gives room for a "Independence of Irrelevant Alternatives" problem to creep in. Many methods suffer from this IIA problem (which says that the Winner shouldn't change when some other candidate sits out) and it may be too much to expect that we can make IIA hold in our recursion, yet in a way a weak variant of IIA is the whole basis of my idea: Weak version of IIA: The winner shouldn't change if the worst candidate is thrown out. This seems like a reasonable requirement for a decent method. The unsimplified version implicitly uses a slightly stronger version (but still close to the weak version): The winner shouldn't change if the worst candidate or next to the worst candidate is thrown out. In this simplified version we're using a much stronger version of IIA: The winner shouldn't change if the Seed Loser is thrown out (unless the winner is the seed loser). Forest On Tue, 27 Feb 2001, Forest Simmons wrote: > Tony, > > here's a simpler version of the Recursive Elimination Supervisor, > based on a suggestion of yours. > > Step 1. Use the seed method in reverse to find the "Seed Loser" SL, from > among the N candidates. > > Step 2. While the SL sits out, recursively supervise the seed method to > find an N-1 stage recursive winner RW from among the N-1 remaining > candidates. > > Step 3. Compare SL and RW directly. Whichever is better is the N stage > recursive winner. In case of a tie between these two, choose RW. > > > Forest > >
Re: [EM] Recursive Elimination Supervisor
Tony, here's a simpler version of the Recursive Elimination Supervisor, based on a suggestion of yours. Step 1. Use the seed method in reverse to find the "Seed Loser" SL, from among the N candidates. Step 2. While the SL sits out, recursively supervise the seed method to find an N-1 stage recursive winner RW from among the N-1 remaining candidates. Step 3. Compare SL and RW directly. Whichever is better is the N stage recursive winner. In case of a tie between these two, choose RW. Forest
Re: [EM] Recursive Elimination Supervisor
Interesting. This might turn out to be the best IRV mitigation. Not that IRV advocates have ever accepted any mitigation. As I always say, they seem determined to impose all the worst of IRV on the voting public. But mitigations such as this should be offered to them, so that we can later show that not only did they know about IRV's problems, but they were also offered a number of mitigation compromises, none of which they accepted. Then there's always the possibility that a new method can turn out to be one of the best, or maybe the best, in some important regard. It would be a mistake to take it as certain that the best methods known so far will always be the best known methods, and so sometimes we've checked out new methods to find out if they challenge Condorcet for the title of the best. So far none of them have, but when a new method looks good, it should of course be checked out, and so let's find out if this particular new method is up there with the best. Mike Ossipoff _ Get your FREE download of MSN Explorer at http://explorer.msn.com
